: : : : "Devious Derivations: Popular Misconceptions -- and More than 1,000 True Origins of Common Words and Phrases" by Hugh Rawson (toExcel, Iuniverse.com, 1994, 2000). This reference has some new information on the origins listed here (new information in parenthesis), new origins and what could be the actual origin.

: : : : New origins from Mr. Rawson's book:
: : : : 12. The abbreviation is for Oberst Kommandant, German for "Colonel in Command," used by either -- take your pick -- a General Schliessen or Baron von Steuben when initialing letters and orders during the American Revolution.
: : : : 13. It comes from the name of a freight agent, Obadiah Kelly, whose initials were widely disseminated on bills of lading.
: : : : 14. The abbreviation is for Open Key, popularized by telegraphers in the 1860s.
: : : : 15. It comes from the names of Lords Onslow and Kilbracken, who initialed bills after they were read and approved in England's House of Lords.
: : : : 16. From a misreading of "Order Recorded" on official documents.
: : : : 17. Or from Finnish "oikea," correct.
: : : : 18. From the Greek "olla," all, plus "Kalla," good.

: : : : Professor Allen Walker Read of Columbia University, "finally unveiled its (O.K.'s) origins in a series of magisterial articles in 'American Speech' in 1963 and 1964.What Professor Read discovered was that the abbreviation arose in a humorous manner at a time when Americans were indulging in a great deal of wordplay, including abbreviations, acronyms, puns and intentional mispronunciations and misspellings. The earliest example of O.K. that he unearthed (and it is so far still the oldest known specimen) is from the Boston 'Morning Post' of March 23, 1839. It appears in connection with a note by the paper's editor, Charles Gordon Greene, about a visit to New York of some members of the local Anti-Bell-Ringing Society. (The A.B.R.S., as it was usually known, was itself something of a joke, having been formed the previous year to oppose -- its name to the contrary -- an ordinance of the Boston Common Council against ringing dinner bells.) In an aside, Mr. Greene suggested that if the Bostonians were to return home via Providence, they might be greeted by one of his rivals, the editor of that city's 'Journal,' who 'would have the 'contribution box,' et ceteras, o.k. -- all correct -- and cause the corks to fly, like sparks, upward.'.Thus, it appears that O.K. was invented, possibly by Greene, as an abbreviation of the jocular 'Oll' or perhaps 'Orl korrect,' meaning "All right.' This explanation would seem farfetched, except for Read's finding that it dovetails with such coinages of the period as O.W. for 'All Right,' as though spelled 'Oll Wright' (this appeared in the Boston 'Morning Post' in 1838, the year before O.K.'s debut); K.G. for 'No Good'; and K.Y. for 'No Yuse.'."

: : : : So it looks like origin No. 4 is correct. Professor Read does believe that O.K. "certainly was popularized" by the use of Martin Van Buren's nickname, Old Kinderhook, (See No. 5) during the presidential campaign of 1840.

: : : : The Word Detective online does mention Mr. Rawson's book but not the theory about Mr. Greene being the originator. Maybe my edition of "Devious Derivations" is newer.

: : : How did they get K.G. from No Good and K.Y. from No Yuse?

: : It was a joke, deliberate misspelling. Know = no

: The good professor died recently.

Among etymologists, Allen Walker Read, 96, who died Wednesday in New York, was known as the man who discovered the original usage of "OK."
His quest began in 1941 when, as a former research assistant for the Dictionary of American English, he wanted to help out his friends still working there by finding an earlier reference to OK to "add some freshness to their entry."
[.]
Years later, Read dug deeper and found an earlier source for the word - a Boston newspaper in 1838 that playfully used initials for such phrases as G.T.D.H.D. (give the devil his due) and O.K.K.B.W.P. (one kind kiss before we part). In this vernacular, O.K. stood for "all correct," spelled just for fun as "oll korrect." Old Kinderhook and "oll korrect" have long been the first accepted sources for the word.
[.]
-- Claudia Luther, "Etymologist Allan Walker Read, 96," Newsday, October 21, 2002